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# Taylor Polynomials Lab

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Author: Beth Barsness
##### Description:
1. Students will start with linear approximations to the cosine curve and then find a quadratic approximation. They will see the connections between all the derivatives and the coefficients of the Taylor polynomials.
2. Students will develop the formula for the general Taylor polynomial and then use their formula to fit 4 approximations to the cosine curve centered at zero.

This lab is an introduction to the concept of approximating any function with a power series using Taylor polynomials.  The students will fit polynomials to non-polynomial functions and discover the development of that Taylor polynomial associated with the function.  After this activity, students will have a better understanding of Taylor polynomials and why they are generated the way they are generated.  Taylor polynomials have always been in at least one free response question on the AP exam and are heavily embedded in the multiple choice portion as well.

Length of time needed: 3 class periods (60 minutes each)

This lesson was written by Lana Golembeski.

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Tutorial

## Lesson Plan

This lesson plan can be downloaded to your computer as a PDF document. If you would like to edit this document for your classroom needs, go to the "Handouts and Materials" section and click on the corresponding link.

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Source: Lana Golembeski